Question

A aand B can do a piece of work in 12 days B and C can do a piece of work in 15 days while C and A can do it in 20 days
(a) How long will they take working together to complete the work?
(b) How long will each of them takes working individually to complete the work

Answer 1

A+B=12days. ......1
B+C=15 days. ......2
C+A=20 days. .....3
adding 1 and 2 and 3 we get
A+B+C+A+B+C=(12+15+20)days
2(A+B+C)=47 days
A+B+C=47/2days
hence A, Band C together can do work in 23.5 days

Answer 2

A and B can do a work in 12 days
B and C can do a work in 15 days
C and A can do a work in 20 days

L.C.M of 12,15,20=60
so,total work of (A and B)+(B and C)+(C and A) is 60.

1 day work of A and B is =60/12=5 unit
1 day work of B and C is =60/15=4 unit
1 day work of C and A is =60/20=3 unit

(A and B,B and C,C and A) 1 day total work=A+B+B+C+C+A=2(A+B+C)=5+4+3
A+B+C=12/2=6

so,A+B+C=6,A+B=5,B+C=4,C+A=3
A=(A+B+C-B+C)=(6-4)=2
B=(A+B+C-C+A)=(6-3)=3
C=(C+A-A)=(3-2)=1

1. Question ans

together complete the work=60/6=10 days

2. Question ans

A can complete the work=60/2=30 days
B can complete the work=60/3=20 days
C can complete the work=60/1=60 days